Abstract
We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings.
This work has been supported by ArcelorMittal, Maizières Research, Measurement and Control Dept., France.
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References
Angulo, J.: Pseudo-morphological image diffusion using the counter-harmonic paradigm. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010, Part I. LNCS, vol. 6474, pp. 426–437. Springer, Heidelberg (2010)
Bullen, P.: Handbook of Means and Their Inequalities, 2nd edn. Springer (1987)
Cireşan, D.C., Meier, U., Masci, J., Schmidhuber, J.: A committee of neural networks for traffic sign classification. In: International Joint Conference on Neural Networks, IJCNN 2011 (2011)
Cireşan, D.C., Meier, U., Masci, J., Schmidhuber, J.: Flexible, high performance convolutional neural networks for image classification. In: International Joint Conference on Artificial Intelligence, IJCA I2011 (2011)
Ciresan, D.C., Giusti, A., Gambardella, L.M., Schmidhuber, J.: Deep neural networks segment neuronal membranes in electron microscopy images. In: NIPS (2012)
Ciresan, D.C., Meier, U., Gambardella, L.M., Schmidhuber, J.: Convolutional neural network committees for handwritten character classification. In: ICDAR, pp. 1250–1254 (2011)
Harvey, N.R., Marshall, S.: The use of genetic algorithms in morphological filter design. Signal Processing: Image Communication 8(1), 55–71 (1996)
Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture of monkey striate cortex. The Journal of Physiology 195(1), 215–243 (1968)
LeCun, Y.: Une procédure d’apprentissage pour réseau à seuil asymétrique. In: Proceedings of Cognitiva, Paris, vol. 85, pp. 599–604 (1985)
Masci, J., Meier, U., Cireşan, D.C., Fricout, G., Schmidhuber, J.: Steel defect classification with max-pooling convolutional neural networks. In: International Joint Conference on Neural Networks (2012)
Nakashizuka, M., Takenaka, S., Iiguni, Y.: Learning of structuring elements for morphological image model with a sparsity prior. In: IEEE International Conference on Image Processing, ICIP 2010, pp. 85–88 (2010)
Pessoa, L.F.C., Maragos, P.: Mrl-filters: a general class of nonlinear systems and their optimal design for image processing. IEEE Transactions on Image Processing 7(7), 966–978 (1998)
Salembier, P.: Adaptive rank order based filters. Signal Processing 27, 1–25 (1992)
Salembier, P.: Structuring element adaptation for morphological filters. J. of Visual Communication and Image Representation 3(2), 115–136 (1992)
Scherer, D., Müller, A., Behnke, S.: Evaluation of pooling operations in convolutional architectures for object recognition. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010, Part III. LNCS, vol. 6354, pp. 92–101. Springer, Heidelberg (2010)
Serra, J.: Image analysis and mathematical morphology. Academic Press, London (1982)
Soille, P.: Morphological Image Analysis: Principles and Applications. Springer (1999)
Turaga, S.C., Murray, J.F., Jain, V., Roth, F., Helmstaedter, M., Briggman, K., Denk, W., Seung, H.S.: Convolutional networks can learn to generate affinity graphs for image segmentation. Neural Comput. 22(2), 511–538 (2010)
van Vliet, L.J.: Robust local max-min filters by normalized power-weighted filtering. In: Proc. of IEEE ICPR 2004, vol. 1, pp. 696–699 (2004)
Werbos, P.J.: Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Ph.D. thesis, Harvard University (1974)
Wilson, S.S.: Training structuring elements in morphological networks. In: Mathematical Morphology in Image Processing, ch. 1, pp. 1–42. Marcel Dekker (1993)
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Masci, J., Angulo, J., Schmidhuber, J. (2013). A Learning Framework for Morphological Operators Using Counter–Harmonic Mean. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_28
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DOI: https://doi.org/10.1007/978-3-642-38294-9_28
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